In the context of hand and finger rehabilitation, kinematic compatibility is key for the acceptability and clinical exploitation of robotic devices. Different kinematic chain solutions have been proposed in the state of the art, with different trade-offs between characteristics of kinematic compatibility, adaptability to different anthropometries, and the ability to compute relevant clinical information. This study presents the design of a novel kinematic chain for the mobilization of the metacarpophalangeal (MCP) joint of the long fingers and a mathematical model for the real-time computation of the joint angle and transferred torque. The proposed mechanism can self-align with the human joint without hindering force transfer or inducing parasitic torque. The chain has been designed for integration into an exoskeletal device aimed at rehabilitating traumatic-hand patients. The exoskeleton actuation unit has a series-elastic architecture for compliant human-robot interaction and has been assembled and preliminarily tested in experiments with eight human subjects. Performance has been investigated in terms of (i) accuracy of the MCP joint angle estimation through comparison with a video-based motion tracking system, (ii) residual MCP torque when the exoskeleton is controlled to provide null output impedance and (iii) torque-tracking performance. Results showed a root-mean-square error (RMSE) below 5 degrees in the estimated MCP angle. The estimated residual MCP torque resulted below 7 mNm. Torque tracking performance shows an RMSE lower than 8 mNm in following sinusoidal reference profiles. The results encourage further investigations of the device in a clinical scenario.